mploys 0. ero. Į word counted es, becalled Figure es not mbers prin ced at 3 and cimal $,"or er the order, ch is thus place, er of tens and units to write together, we put the number of tens in the tens' place, and of units in the units' place; thus, thirty-six, or three tens and six units, is written 36. A collection of ten tens is called one hundred, or a unit of the third order, and is represented by 1 in the third or hundreds' place, (100.); two hundreds are represented by 2 in the hundreds' place, (200.); three hundreds by 3 in the hundreds' place, (300.); etc. A collection of ten hundreds is called one thousand, or, a unit of the fourth order, and is represented by 1 in the fourth or thousands' place (1000.); two thousands are represented by 2 in the thousands' place (2000.); etc. 4. 5. Thousands. 19. Read the following: 1. 86. 2. 132. 3. 6321. 7862. 99. 7632. The above represents seven thousands, six hundreds, three tens, and two units, and is read, "Seven thousand six hundred thirty、 two." EXERCISES. 6. 7. 8. 9. 10. 428. 1302. 6006. 7801. 541. QUESTIONS. What is the first place at the left of the decimal point called? What is the second place at the left called? The third ? How many units make one ten? How many tens make one hundred? How many hundreds make one thousand? How many units make one hundred ? How many units make one thousand? How many tens make one thousand? What are units of the first order called? Ans. Simple units. What are units of the second order called? Of the fourth? Of the third ? In 7632 how many tens, and what number remains? How many hundreds, and what remains? How many thousands? REMARK. The number of units of any order is sometimes called a term; thus, the terms of 632 are 6 hundreds, 3 tens, and 2 units. 21. NUMERATION TABLE. 22. The fifth place from the decimal point towards the left is the ten thousands' place, each ten-thousand being equal to ten of the thousands; the sixth place is the hundred thousands' place, each hundred thousand being equal to ten ten-thousands; and so on, each unit of any order being equal to ten units of the order immediately preceding. We now see that the number of units of any order is expressed by the figure, and the order of units by the place which the figure occupies; or, in other words, the value represented by any decimal he third? undred? its make ow many r called? ed? Of ɔw many called a 1st. Units. Decimal point. the left to ten place, and so order ressed ch the y any figure depends upon the figure itself, and upon the place which that figure occupies. Thus, 2 in the first place means simply two (that is, two units); in the second place, it means two tens, or twenty; in the third place, two hundreds. 23. Since, by this method of writing numbers, the value represented by a significant figure increases as that figure is removed towards the left, and decreases as it is removed towards the right, by a scale of tens, the system is called the Decimal System, from the Latin word decem, which signifies ten. NOTE. The reason for calling the dot (Art. 18) a decimal point must now be obvious. This point is not always written, but, when not writtèn, it is always understood. 24. By examining the table (Art. 21), we find it separated by commas into groups of three places each. These groups are called periods, the first period being that of units; the second that of thousands; the third, millions; the fourth, billions, etc. Thus we have simple units, tens of units, and hundreds of units; units, tens, and hundreds of thousands; units, tens, and hundreds of millions; etc. 25. EXERCISES ON THE TAble. 1. Give the names of the first two periods from the decimal point, reading them towards the left; towards the right. Give the names of the first three periods in the same way; of the first four; five; six; seven. What is the second period called? third? sixth? seventh ? fourth? fifth.? 2. In which period are found thousands ? millions? simple units? trillions? billions? quintillions? quadrillions? ten 3. In which place of what period are found tens of units? thousands? hundred-thousands? millions? hundreds of units? thousands? billions? hundred-millions? ten-billions? ten-millions? quadrillions? ten-quintillions? hundred-billions? hundred-trillions? quintillions? ten-quadrillions? ten-trillions? hundred-quadrillions ? trillions? hundred-quintillions? 4. Name the order of units of each number in paragraph 3. Ans. Tens are of the second order, thousands of the fourth order; etc. 5. What order of units is found in the first place of the second period? Ans. Fourth order, or thousands. In the third place of the first period? In the second place of the third period? In the third place of the fourth period? In the first place of the fifth period? In the third place of the sixth period? In the second place of the seventh period? In the third place of the third period? In the first place of the seventh period? In the second place of the fourth period? In the first place of the sixth period ? 6. In 6480921 how many tens, and what remains? Ans. 648092 tens, and 1 unit remaining. How many hundreds, and what remains? Ans. 64809 hundreds, and 21 remaining. How many millions, and what remains? thousands? ten-thousands ? hundred-thousands? 26. The names of the periods employed to express numbers higher than Quintillions are, in their order from Quintillions, Sextillions, Septillions, Octillions, Nonillions, Decillions, Undecillions, Duodecillions, Tredecillions, Quatuordecillions, Quindecillions, Sexdecillions, Septendecillions, Octodecillions, Novendecillions, Vigintillions, etc. 27. To read numbers, observe the following RULE. Beginning at the units' place, point off the expression into periods of three figures each; then begin at the left, and read each period in order from left to right, giving after each, excepting the last, the name of the period. EXERCISES. 28. Read or write in words the following: 361. 786. 3261. 96321. 9301. 80021. 654237. 9326429. 9000200. 86320029. 324867. 81402020. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. See Dictation Exercises, Key. 13. 14. 15. 1122334455. 16. 3670980347. 17. 9008007006. 18. 12400496623. 245607000000. 19. 20. 94632748632. 1781006390800. 21. 22. 62876432019623 23. 753248734762869. 24. 943300896402798. 987654321. 89743208. 29. Name the terms in the first example above, commencing with units (Art. 20, Remark). Ans. One unit, six tens, three hundreds. Name the terms in the second example. In the third. In the other examples, in their order. Read from the Table (Art. 21), the number represented by the first six figures from the decimal point; the first eight; the first ten; nine; twelve; fifteen; seventeen; twenty; fourteen; eighteen. 30. To write numbers, observe the following RULE. Beginning with the highest period, write the figures of each period in their order from left to right, filling vacant places with zeros. 31. EXERCISES. Write the following:- 2. Seven thousand eighty-nine.. 3. Eighteen thousand eighteen. 4. Nine hundred thousand sixteen. Ans. 364. Ans. 7089. 5. Four hundred twenty thousand, six hundred eighty-three. 6. Eight hundred ten thousand, two hundred four. 7. Two hundred fifty-nine thousand, seventy. 8 Forty-five million, seven hundred thousand, two hundred fifty one. 9. Nine hundred one million, two hundred eighteen thousand, twenty-two. 10. Three billion, thirty-seven million, nine hundred six thousand, two hundred. 16. Eighteen billion, four.. 17. Forty million, eight hundred thousand. 11. Two hundred thirty-four million, eight hundred sixty-three thousand, three hundred eighty-nine. 12. Seventeen billion, seven hundred fifty-nine million, ninety thousand, sixty-seven., 13. Three hundred thirty-three quadrillion, seven hundred seventynine billion, three hundred thousand, two. 14. Nine hundred ten quadrillion, four million, three thousand. 15. Fifty-four quintillion, eighty-three quadrillion, nine hundred million, seventeen thousand, one hundred eighty-two. |